I might agree with your second statement (although I suspect I might mean something different by a skills-based system), but probably do not with your first. If all that 15th level character does is fight just like a 14th level one and cast spells just like a 1st level one, this multiclassing is useless, since the gain in versatility is far outweighed by the loss in effectiveness, given that the party will probably be facing 15th-level adversaries, who will most likely shrug off first level spellcasting and dominate against a lower-level fighter.
I really disagree with this kind of argument. First of all, that "the gain in versatility is far outweighted by the loss in effectiveness" is just an assumption, because it all depends on what exactly that level is Wizard is granting, and what the (missed) level in Fighter would have granted. In the 3e system you may be right, because a missed level in Fighter can mean 1 point of BAB lost, and even worse a missed level in Wizard can mean 1/2 spellcasting levels lost. But that happens
in that system, and does not have to happen in all system. All the point is that we should have a system capable of making the two choices equally good, or as close as possible. The bounded accuracy of 5e already gives a somewhat better starting point for this compared to 3e.
Second, if it's really impossible to make them equally good at combat once the core principles of the game (such as attack bonus advancement rates or spellcasting levels) are set, even then it doesn't mean that this multiclassing will be useless, only that it will be
subpar and only
in combat. You don't want to lose even a 5% effectiveness in combat? Don't multiclass, or at least don't multiclass with this specific combination, but the combination may be well worth its price in someone else's game where combat is just one pillar and not
the pillar. If 1st level spells are well designed, taking one level of Wizard might mean to add 3-4 good capabilities to the whole group: it depends on a lot of variable of course, if you already have a full Wizard who knows all spells (or covers all spells
types at least) taking a Wizard level is probably adding nothing to the party. But if you don't already have that, or you have a Wizard who only blasts area damage spells, adding to the party even something as simple as telekinesis, light, and minor illusions can unlock new tactics. If you only have a combat game, then of course not so much...